.\" Copyright (c) 2006 Apple Computer
.\"
.Dd December 11, 2006
.Dt CSINH 3
.Os BSD 4
.Sh NAME
.Nm csinh
.Nd complex hyperbolic sine function
.Sh SYNOPSIS
.Fd #include <complex.h>
.Ft double complex
.Fn csinh "double complex z"
.Ft long double complex
.Fn csinhl "long double complex z"
.Ft float complex
.Fn csinhf "float complex z"
.Sh DESCRIPTION
.Fn csin "z"
computes the hyperbolic sine of the complex floating-point number
.Fa z .
.Pp
For all complex floating point numbers z,
.Bd -literal -offset indent
csinh(conj(z)) = conj(csinh(z)),
.br
csinh(-z) = -csinh(z).
.Ed
.Sh SPECIAL VALUES
The symmetries of csinh() are used to abbreviate the specification of special values.
.Pp
.Fn csinh "0 + 0i"
returns 0 + 0i.
.Pp
.Fn csinh "0 + inf i"
returns 0 + NaN i, and raises the invalid flag.
.Pp
.Fn csinh "0 + NaN i"
returns 0 + NaN i.
.Pp
.Fn csinh "x + inf i"
returns NaN + NaN i, and raises the invalid flag, for finite nonzero x.
.Pp
.Fn csinh "x + NaN i"
returns NaN + NaN i, for finite nonzero x.
.Pp
.Fn csinh "inf + 0i"
returns inf + 0i.
.Pp
.Fn csinh "inf + yi"
returns inf * cis(y), for finite positive y, where cis(y) = cos(y) + i*sin(y).
.Pp
.Fn csinh "inf + inf i"
returns inf + NaN i, and raises the invalid flag.
.Pp
.Fn csinh "inf + NaN i"
returns inf + NaN i.
.Pp
.Fn csinh "NaN + 0i"
returns NaN + 0i.
.Pp
.Fn csinh "NaN + yi"
returns NaN + NaN i, for nonzero numbers y.
.Pp
.Fn csinh "NaN + NaN i"
returns NaN + NaN i.
.Sh NOTES
.Sh SEE ALSO
.Xr csin 3
.Xr complex 3
.Sh STANDARDS
The
.Fn csinh
function conforms to ISO/IEC 9899:1999(E).